Mfcttrf

Please consider this MWE:

documentclassarticle
usepackage[english]babel
usepackage[utf8]inputenc
usepackage[T1]fontenc
usepackage[a4paper,margin=1in,footskip=0.25in]geometry
usepackageamssymb
usepackageamsmath
usepackagemathtools
usepackageamsmath

begindocument
[
f(t)=begincases
 2t+1&textif (0leq tleq2),\
 hrulefill&textif (_ <t<_),
 endcases
]
enddocument

How can we align the last two _ to position them at the same height as hrulefill? Something like:

Also we need to position the <, > and the last t with the above.

Thanks!!

The hrulefill command expands to

leavevmode leaders hrule hfill kern z@`

So one way to do what you want is to use hrule, or better rule, instead of _. If you define

newcommandblankrule2mm0.4pt

then you can use it to produce:

Here is the full code:

documentclassarticle
usepackage[english]babel
usepackage[utf8]inputenc
usepackage[T1]fontenc
usepackage[a4paper,margin=1in,footskip=0.25in]geometry
usepackageamssymb
usepackageamsmath
usepackagemathtools
usepackageamsmath
newcommandblankrule2mm0.4pt

begindocument
[
f(t)=begincases
 2t+1&textif (0leq tleq2),\
 hrulefill&textif (blank <t<blank),
 endcases
]
enddocument

Since you are already using mathtools I'd also recommend using the cases* environment so that you can omit the text... commands when using cases. Unfortunately, hrulefill does not work inside a cases* environment, so here is a fancier version of the blank command that takes an optional argument that sets the length of the blank to the length of the supplied content:

documentclassarticle
usepackageamsmath
usepackagemathtools
usepackageamsmath
newcommandblank[1][$_$]rulewidthof#10.4pt

begindocument
[
f(t)=begincases*
 2t+1&if (0leq tleq2),\
 blank[$2t+1$]&if (blank <t<blank),
 endcases*
]
enddocument

The output is similar to before. except that the default length of blank is now the length of _, which is slightly shorter.

I would just work with phantoms in this case.

documentclassarticle
usepackage[english]babel
usepackage[utf8]inputenc
usepackage[T1]fontenc
usepackage[a4paper,margin=1in,footskip=0.25in]geometry
usepackageamssymb
usepackageamsmath
usepackagemathtools
usepackageamsmath

begindocument
[
f(t)=begincases
 2t+1&textif (0leq tleq2),\
 underlinephantom2t+1&textif (underlinephantom0 <t<underlinephantom2),
 endcases
]
enddocument